IJCT 1(5) 305-307
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Transcript of IJCT 1(5) 305-307
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7/25/2019 IJCT 1(5) 305-307
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Indian Journal of Chemical Technology
Vol. 1, September 1994. pp. 305-307
Short Communication
AsbHtos lid
Coolant out
If coil
Thermocole
Insulation
Teflon stirrer
Coolant
in
la D I 1
Motor control
Speed control
d .10414mm
T
Dc
Dc-aa-omm
OI~79-8mm
H~aO-Omm
l7
Oi
P 200mm
11
0
,
Cooling of a viscous liquid using a half-coil
jacket
Y Pydisetty & N S Jayakumar
Department of Chemical Engineering, D D Institute of
Technology, Nadiad 387 001, India
Cooling of a hot viscous glycerine liquid using wa-
ter as coolant flowing through a half-coil jacket has
been studied experimentally in a batch stirred system
to investigate the individual as well as the overall
time-variant heat transfer coefficients.
In an indirect heat transfer system jackets or coils
are used for heating cooling or temperature con-
trol of a chemical reaction. Coils are more suit-
able than jackets since coil geometry offers higher
heat transfer rates and ensure close temperature
control. There are some reports on heat transfer
in a limpet coil, also known as half-coil' . An
equation has been derived for heat transfer effi-
ciency of a limpet coil comparing it with a jacket-
ed vessel for both unsteady state
I
and steady
state
conditions. The present experiment has
been carried out using a half-coil jacket since the
data available in such a unit is little.
The experimental set-up and coil geometry
used in the present study are shown in Fig. 1,
while Table 1 shows the experimental conditions.
The experiments were conducted by varying the
Coil geometry
Fig. 1- Experimental set-up and coil geometry
flow rate of the cooling water and the initial tem-
perature of hot glycerine. The transient tempera-
ture data on the vessel
T
h
)
as well as on the coil
side (~) are shown in Fig. 2.
Results and discussion-The
temperature vs
time data for fixed time intervals obtained from
Fig. 2 have been used to calculate the corre-
sponding logarithmic mean temperature differ-
ence, shown in Table 2. The individual and over-
all heat transfer coefficients have been calculated
from heat balances assuming negligible heat losses
from the vessel lid, bottom and side, uniform tem-
perature throughout the bath inside the vessel,
steady flow of coolant throughout the experiment
and constant wall temperature throughout the
wall thickness. Heat balance on bath side gives:
d J
- VPh C
ph
-= hiAi (~T )In
dt
... (1)
Heat balance on coil side gives:
qpcCpc(~- ~i=hoAo AT ln ... 2
hi, obtained from Eq. (1) is corrected for viscos-
ity by wall temperature calculations. The logarith-
Table I-Experimental conditions of the present study
Volume of hot glycerine,
V :
400 x 10 - 6 m
3
Flow rate of cooling water, qx 10
6
: 1.67-6.00 m
3
/s
Initial temperature of hot glycerine,
Thi :
45-96C
Thickness of the vessel, X w : 0.0015 m
Length ofthe limpet coil, L 1.525 m
[-I
A
[
fl
[-)
.
[8
Fig. 2-Experimental transient temperature data
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306
INDIAN J.CHEM. TECHNOL., SEPTEMBER 1994
Table 2-ResuIts on heat transfer film coefficients
E-l
q=6.0x 1O-6m3/s; T
hi
=64.0C; T.:i=27.0C; T,.=32.0C
t.S
~nn C
t C
h;,W/m2K
h , W/m2 K
U
oe
,
W/m
2
K
120
47.73 58.9
204.l3
199.30
114.40
240
38.89 53.0
197.97
171.95
\04.02
360 32.29
47.7 169.58
143.36
89.20
480 27.60 45.1 167.89 111.85 76.55
600 23.50
43.0 174.68 87.57 64.34
Table 3-Comparison of experimental and predicted Nusselt number
Expt. No.
U c'
W/m
K
De
Nllc NlIp
E,
deviation
E-1 89.62 435.00 0.914 0.873
77.40
4.5
E-2 126.55
221.48
1.294
1.223 75.70
5.5
E-3
156.03 125.64
1.582
1.624 74.90
- 2.7
E-4 \05.92
386.65 1.090 0.926 76.50 15.0
E-5 74.33 389.87 0.765
0.922
711.40
- 20.5
E-6 94.68 274.03 0.975
1.099
77.10 - 12.7
E-7
116.18 236.78
1.190 1.183
76.10
0.6
mic mean temperature difference in Eq. (2) IS
given by
(~T)ln=(1h- 7;,;)- 1h- 7;,)
In (1h-
7 ; , ;
1h-7;,
... (3)
The properties p; and Cpc are taken' at the mean
temperature of 4j and maximum 4 for any ex-
periment. The properties Ph and C
ph
are taken' at
the bath temperature Th at any time, t. In the
present study, as a viscous liquid was used inside
the vessel, the wall temperature was found to be
different from the bath temperature. Hence, the
inside heat transfer film coefficient is modified for
viscosity correction by multiplying with a factor of
flhl
flhw)O.14.
The transport property,
flhw
is taken'
at the wall temperature, T; which is obtained
from the heat balance between the wall and hot
liquid, given as
... 4)
For egimation of wall temperature, it is assumed
that Aw equals to A
o
Rearranging the terms in
Eq. (4) the wall temperature, T; is obtained as
h ;Xw Th+~) t
x; o.n
(5 )
The corrected inside heat transfer film coefficient,
h i
is given as
h i= h j flh 1flh w )o .1 4 ...
6)
The experimental overall heat transfer coefficient
based on outside area, U
oe
is calculated using the
following equation
1 1
x,
1
--=-+---+-- ...7)
UoeAo
h i
Ai . KwAw hoAo
where A : . is the logarithmic mean area of the wall.
Table 2 shows the values of
h i,
h o and U oe- As the
present work involves batch heat transfer study,
the time-averaged experimental overall heat trans-
fer coefficient, [Joe is calculated for each experi-
ment as follows
M
I
u oe tJ ~ t J
- J=1
U
oe
=~M ----
I tJ ~t J
J-1
... (8)
In all the above calculations an equivalent diame-
ter for coil side, D
eq
has been defined using hy-
draulic mean radius, r
H
as follows
o; =
4rH
=
l l : 2
d ...
9)
Experimental Nusselt number is related to Dean
number as
Nu= 18.2 (Det.5
... (10)
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SHORT COMMUNICATION
307
where Dean number,
Deis
defined as
De= De~cV : t
5
The power for Dean number in Eq. (10) is ob-
tained from a plot of
NU
e
versus
De.
Table 3
shows the values of
De,
[Joe,
NU
e
and
Nu
p
which
indicates that the experimental and predicted
Nusselt number are in good agreement with a
standard deviation of 0.104 and a variance of
0.0108. Moreover, the percentage deviation of
each experiment is reported in Table 3. The rela-
tive heat transfer efficiency of half-coil jacket
compared to jacketed vessel,
E
in the present
study is obtained' using the following equation'
... (11)
E= 2 + tanh mL)
3 mL
where
m
2
=
[J
ol
x;
The values of the efficiency, E (Eq. (12)) are re-
ported in Table 3 with an average efficiency of
77%.
Conclusions-Cooling of a viscous liquid has
been studied experimentally. The viscosity correc-
tion for inside heat transfer film coefficient has
been done using the calculated wall temperature.
The experimental Nusselt number is related to
Dean number as
... (12)
Nu= 18.2 {De -O.5
omenclature
Ai
=
inside heat transfer area, m
2
A cross-sectional area of the limpet, m
2
Ao =heat transfer area on coil side, m?
Cpc =specific heat of the coolant, J/kg K
C
ph
=specific heat of the hot liquid, J/kg K
h i
=
inside film heat transfer coefficient at any time, t,
W/m2K
h u =outside film heat transfer coefficient at any time, t,
W/m
K =thermal conductivity of the coolant, W/m K
K; =thermal conductivity of the glass wall, W/m K
I
=time corresponding to Jth reading, s
~/ h
=time interval between Jth and J- 1 th readings, s
T =ambient temperature, C
Tci =feed temperature of the coolant, C
v =average velocity of the coolant (q/A ),m1s
flh =viscosity of the hot liquid at the bath temperature kg/
ms
o;
=
density of the coolant, kg/rn?
Ph
=
density of the hot liquid, kg/m
N U
e
=experimental Nusselt number [Joe Dei K
Nu; =predicted Nusselt number (Eq. (10))
eferences
1 Biswas D K
Panthaki K M, Chem Age India, 28 (1977)
733.
2 Joshi M V, Process equipment design, 1st ed (The Macmil-
lan Company of India Ltd, New Delhi), 1976,222.
3 Kneale M,
Trans Inst Chem Eng,
47 (1969) 1279.
4 Marzi Maurizio,
Ital Chem Process,
17(5) (1989) 43;
Chem
Abstr,111 (1989) 156662p.
5 Pavlov K F, Rornankov P G Noskov A A, Examples and
problems to the course of unit operations of chemical
engi-
neering(Mir Publishers, Moscow), 1979, 548, 571.